The adiabatic single‐crystalline elastic constants of pure niobium, Nb‐Zr, Nb‐Hf, and Nb‐W alloys were determined in the temperature range 77–298 °K. An unusual temperature dependence was noted in the Nb‐rich alloys which may be related to the shape of the Fermi surface. Zr and Hf alloying additions decrease the value ofC′, which indicates decreasing bcc lattice stability. The values of the elastic anisotropy ratioC44/C′ follow the behavior predicted by Fisher, which indicates that the elastic shear moduli are closely related to the filling of thedband. The Debye temperatures &Vthgr;Dwere calculated, and W additions tend to increase &Vthgr;D, while Zr and Hf lower &Vthgr;D.